The Kerala School was a school of mathematics and astronomy founded by Madhava in Kerala (in South India) which included as its prominent members Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. It flourished between the 14th and 16th centuries and has its intellectual roots with Aryabhatta who lived in the 5th century. The lineage continues down to modern times but the original research seems to have ended with Narayana Bhattathiri (1559-1632). These astronomers, in attempting to solve problems, invented revolutionary ideas of calculus. They discovered the theory of infinite series, tests of convergence (often attributed to Cauchy), differentiation, term by term integration, iterative methods for solution of non-linear equations, and the theory that the area under a curve is its integral. They achieved most of these results up to several centuries before European mathematicians. Madhava (माधव) of Sangamagrama (1350-1425) was a major mathematician of the Kerala school who is considered the father of mathematical analysis for having taken the decisive step from the finite procedures of ancient mathematics to treat their limit-passage to infinity, which is the kernel of modern classical analysis. ... Categories: | | ... A map of South India, its rivers, regions and water bodies. ... Parameshvara (परमेश्वर) (1360-1425) was a major mathematician of the Kerala school. ... Neelakanta Somayaji (1444-1545) was a member of the Kerala school of astronomy and mathematics and was a student of Damodara. ... Jyestadeva (1500-1610), was an astronomer of the Kerala school founded by Madhava of Sangamagrama and a student of Damodara. ... Achyuta Pisharati (1550–1621) was a renowned Sanskrit grammarian, astrologer and mathematician of his time. ... This 14th-century statue from south India depicts the gods Shiva (on the left) and Uma (on the right). ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ... Aryabhata (आर्यभट) (Āryabhaṭa) is the first of the great astronomers of the classical age of India. ... // Overview Events Romulus Augustus, Last Western Roman Emperor 410: Rome sacked by Visigoths 452: Pope Leo I allegedly meets personally with Attila the Hun and convinces him not to sack Rome 439: Vandals conquer Carthage At some point after 440, the Anglo-Saxons settle in Britain. ... Events January 15 - Elizabeth I of England is crowned in Westminster Abbey. ... See also: 1632 (novel) Events February 22 - Galileos Dialogue Concerning the Two Chief World Systems is published July 23 - 300 colonists for New France depart Dieppe November 8 - Wladyslaw IV Waza elected king of the Polish-Lithuanian Commonwealth after Zygmunt III Waza death November 16 - Battle of Lützen... Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ... As the degree of the Taylor series rises, it approaches the correct function. ... In the absence of a more specific context, convergence denotes the approach toward a definite value, as time goes on; or to a definite point, a common view or opinion, or toward a fixed or equilibrium state. ... Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Differentiation can mean the following: In biology: cellular differentiation; evolutionary differentiation; In mathematics: see: derivative In cosmogony: planetary differentiation Differentiation (geology); Differentiation (logic); Differentiation (marketing). ... Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ... An iterative method attempts to solve a problem (for example an equation or system of equations) by finding successive approximations to the solution starting from an initial guess. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. ...

Jyeshtadeva consolidated the Kerala School's discoveries in the Yuktibhasa, the world's first calculus text.

The Kerala School also contributed much to linguistics. The ayurvedic and poetic traditions of Kerala were founded by this school. The famous poem, Narayaneeyam, was composed by Narayana Bhattathiri. Ayurveda (आयुर्वेद Sanskrit: ayu—life; veda—knowledge of) or ayurvedic medicine is a comprehensive system of medicine, more than 5,000 years old and based on a holistic approach rooted in Vedic culture. ... Categories: | | ... Narayaneeyam is a devotional Sanskrit work, in the form of a poetical hymn, consisting of 1034 verses (called slokas in Sanskrit). ...

Keralese Mathematicians

Narayana Pandit (c. 1340-1400)

Narayana Pandit, the earliest of the notable Keralese mathematicians, is known to have definitely written two works, an arithmetical treatise called Ganita Kaumudi and an algebraic treatise called Bijganita Vatamsa. He was strongly influenced by the work of Bhaskara II, which proves work from the classic period was known to Keralese mathematicians and was thus influential in the continued progress of the subject. Due to this influence Narayana is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati, titled Karmapradipika (or Karma-Paddhati). It has been suggested that this work was written in conjunction with another scholar, Shankara Variyar, while others attribute the work to Madhava. Narayana Pandit (नारायण पण्डित) (1340-1400) was a major mathematician of the Kerala school. ... Events Europe has about 74 million inhabitants. ... Events Henry IV quells baron rebellion and executes The Earls of Kent, Huntingdon and Salisbury for their attempt to have Richard II of England restored as King Jean Froissart writes the Chronicles Medici family becomes powerful in Florence, Italy Births December 25 - John Sutton, 1st Baron Dudley, Lord Lieutenant of... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ... Wikipedia does not yet have an article with this exact name. ... Shankara Variyar, wrote the celebrated Yuktidipika, a commentary on the Tantra-sangraha of Nilakantha Somayaji. ...

Although the Karmapradipika contains very little original work, seven different methods for squaring numbers are found within it, a contribution that is wholly original to the author. Narayana's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, using the second order indeterminate equation nq² + 1 = p² (Pell's equation). Mathematical operations with zero, several geometrical rules and discussion of magic squares and similar figures are other contributions of note. Evidence also exists that Narayana made minor contributions to the ideas of differential calculus found in Bhaskara II's work. Pells equation is any Diophantine equation of the form where n is a nonsquare integer. ... 0 (zero), alternatively called naught, nil, ought, or nought, is both a number and a numeral. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ...

Narayana has also made contributions to the topic of cyclic quadrilaterals. Subsequent developments of this topic, found in the works of Shankara Variyar and Ganesha interestingly show the influence of work of Brahmagupta. Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ...

Madhava of Sangamagramma (1340-1425)

Madhava is the founder of the Kerala School and considered to be one of the greatest mathematician-astronomers of the Middle Ages. Sadly all of his mathematical works are currently lost, although it is possible extant work may yet be 'unearthed'. It is vaguely possible that he may have written Karana Paddhati a work written sometime between 1375 and 1475, but this is only speculative. All we know of Madhava comes from works of later scholars, primarily Nilakantha Somayaji and Jyesthadeva. Events Europe has about 74 million inhabitants. ... Events Foundation of the Katholieke Universiteit Leuven, Belgium Births John II, Duke of Lorraine (died 1470) Edmund Sutton, English nobleman (died 1483) Deaths January 18 - Edmund Mortimer, 5th Earl of March, English politician (born 1391) March 17 - Ashikaga Yoshikazu, Japanese shogun (born 1407) May 24 - Murdoch Stewart, 2nd Duke of... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ... Events October 24 - Valdemar IV of Denmark dies and is succeeded by his grandson Olaf III of Denmark. ... Events August 29 - Treaty of Picquigny ends a brief war between France and England. ... Nilakantha Somayaji (नीलकण्ठ सोमयाजि) (1444-1544), from Kerala, was a major mathematician and astronomer. ... Jyesthadeva (1500-1575), born in Kerala, was a major mathematician, and author of the 1501 Yukti-bhasa, which was a survey of Kerala mathematics and astronomy that was unique at the time for its exacting proofs of the theorems it presented. ...

His most significant contribution was in moving on from the finite procedures of ancient mathematics to 'treat their limit passage to infinity', which is considered to be the essence of modern classical analysis, and thus he is considered the father of mathematical analysis. Madhava was responsible for a number of discoveries, including the Madhava-Gregory series, Madhava-Newton power series, Euler's series, and the power series for pi (usually attributed to Leibniz). Madhava is responsible for laying the foundations for the development of calculus, which was then further developed by his successors at the Kerala School. Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... Several notable persons have been named James Gregory: James Gregory (astronomer and mathematician) James Gregory (mineralogist) James Gregory (actor) This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... Sir Isaac Newton, PRS (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, and natural philosopher who is regarded by many as the most influential scientist in history. ... In mathematics, a power series (in one variable) is an infinite series of the form where the coefficients an, the center c, and the argument x are usually real or complex numbers. ... Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced oiler) was a Swiss mathematician and physicist. ... Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ... Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ...

Parameshvara (c. 1370-1460)

Parameshvara is known to have been a pupil of Narayana Pandit, and also Madhava of Sangamagramma, who is thought to have been a significant influence. He wrote commentaries on the work of Bhaskara I, Aryabhata and Bhaskara II, and his contributions to mathematics include an outstanding version of the mean value theorem. Furthermore Paramesvara gave a mean value type formula for inverse interpolation of sine, and is thought to have been the first mathematician to give the radius of circle with inscribed cyclic quadrilateral, an expression that is normally attributed to Lhuilier (1782). Parameshvara (परमेश्वर) (1360-1425) was a major mathematician of the Kerala school. ... Events Beginning of the rule of Poland by Capet-Anjou family. ... Events The first Portuguese navigators reach the coast of modern Sierra Leone. ... Bhaskara I, 7th century Indian mathematician, gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhatas work. ... Aryabhata (आर्यभट) Ä€ryabhaá¹­a) is the first of the great astronomers of the classical age of India. ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ... For any function that is continuous on [a, b] and differentiable on (a, b) there exists some c in the interval (a, b) such that the secant joining the endpoints of the interval [a, b] is parallel to the tangent at c. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... 1782 was a common year starting on Tuesday (see link for calendar). ...

Nilakantha Somayaji (1444-1544)

In turn, Nilakantha Somayaji was a disciple of Parameshvara and was educated by his son Damodra]. In his most notable work Tantra Samgraha (which 'spawned' a later anonymous commentary Tantrasangraha-vyakhya and a further commentary by the name Yuktidipaika, written in 1501) he elaborates and extends the contributions of Madhava. Sadly none of his mathematical works are extant, however it can be determined that he was a mathematician of some note. Nilakantha was also the author of Aryabhatiya-bhasa a commentary of the Aryabhatiya. Of great significance is the presence of mathematical proof (inductive) in Nilakantha's work. Nilakantha Somayaji (नीलकण्ठ सोमयाजि) (1444-1544), from Kerala, was a major mathematician and astronomer. ... Events March 1 - Gjergj Kastriot Skanderbeg proclaimed commander of the Albanian resistance April 16 - Truce of Tours. ... Events April 11 - Battle of Ceresole - French forces under the Comte dEnghien defeat Imperial forces under the Marques Del Vasto near Turin. ... 1501 was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar. ...

Jyesthadeva (c. 1500-1575)

Jyesthadeva was a member of the Kerala School, which was founded on the work of Madhava, Nilakantha, Parameshvara and others. His key work was the Yukti-bhasa (written in Malayalam, a regional language of Kerala). Similarly to the work of Nilakantha it is almost unique in the history of Indian mathematics, in that it contains both proofs of theorems and derivations of rules. He also studied various topics found in many previous Indian works, including integer solutions of systems of first degree equations solved using kuttaka. Jyesthadeva (1500-1575), born in Kerala, was a major mathematician, and author of the 1501 Yukti-bhasa, which was a survey of Kerala mathematics and astronomy that was unique at the time for its exacting proofs of the theorems it presented. ... 1500 was a common year starting on Monday (see link for calendar) of the Gregorian calendar. ... Events February 13 - Henry III of France is crowned at Reims February 14 - Henry III of France marries Louise de Lorraine-Vaudémont June 28 - Oda Nobunaga defeats Takeda Katsuyori in the battle of Nagashino, which has been called Japans first modern battle. ... Malayalam (മലയാളം) is the major language of the state of Kerala, in southern India. ... Categories: | | ... Indian contributions to mathematics include 1. ...

Sankara Varman (Early 1800s)

There remains a final Kerala work worthy of a brief mention, Sadrhana-Mala an astronomical treatise written by Sankara Varman serves as a summary of most of the results of the Kerala School. What is of most interest is that it was composed in the early 19th century and the author stands as the last notable name in Keralese mathematics. Events and Trends Beginning of the Napoleonic Wars (1803 - 1815). ...

Possible transmission of Keralese mathematics to Europe

There are a number of publications, including a recent paper of great interest written by D. Almeida, J. John and A. Zadorozhnyy, which suggest Keralese mathematics may have been transmitted to Europe. Kerala was in continuous contact with China, Arabia, and from around 1500, Europe as well, thus transmission would have been possible. There is no evidence by way of relevant manuscripts but the evidence of methodological similarities, communication routes and a suitable chronology for transmission is hard to dismiss. Europe is conventionally considered one of the seven continents which, in this case, is more a cultural and political distinction than a physiogeographic one. ... The Arabian Peninsula The Arabian Peninsula is a mainly desert peninsula in Southwest Asia at the junction of Africa and Asia and an important part of the greater Middle East. ... 1500 was a common year starting on Monday (see link for calendar) of the Gregorian calendar. ...

A key development of pre-calculus Europe, that of generalisation on the basis of induction, has deep methodological similarities with the corresponding Kerala development (200 years before). There is further evidence that John Wallis (1665) gave a recurrence relation and proof of Pythagoras theorem exactly as Bhaskara II did. The only way European scholars at this time could have been aware of the work of Bhaskara would have been through Keralese 'routes'. In mathematics, the Pythagorean theorem or Pythagorass theorem, is a relation in Euclidean geometry between the three sides of a right triangle. ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ...

Although it was believed that Keralese calculus remained localised until its discovery by Charles Whish in the late 19th century, Kerala has in fact been in contact with Europe ever since Vasco da Gama first arrived there in 1499 and trade routes were established between Kerala and Europe. Along with European traders, Jesuit missionaries from Europe were also present in Kerala during the 16th century. Many of them were mathematicians and astronomers, and were able to speak local languages such as Malayalam, and were thus able to comprehend Keralese mathematics. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Vasco da Gama Vasco da Gama Vasco da Gama (IPA: /; born c. ... 1499 was a common year starting on Sunday (see link for calendar) of the Gregorian calendar. ... The Society of Jesus (Latin: Societas Iesu), commonly known as the Jesuits, is a Roman Catholic religious order. ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ... An astronomer or astrophysicist is a scientist whose area of research is astronomy or astrophysics. ... Malayalam (മലയാളം) is the major language of the state of Kerala, in southern India. ...

It is also worth noting that the British East India Company began trading with India sometime between 1600 and 1608, not too long before Europe's Scientific Revolution began. There was also some controversy in the late 17th century between Newton and Leibniz, over how they independently 'invented' calculus almost simultaneously, which sometimes leads to the suggestion that they both may have acquired the relevant ideas indirectly from Keralese calculus. The British East India Company, sometimes referred to as John Company, was a joint-stock company of investors, which was granted a Royal Charter by Elizabeth I on December 31, 1600, with the intent to favour trade privileges in India. ... // Events January January 1 - Scotland adopts January 1st as being New Years Day February February 17 - Giordano Bruno burned at the stake for heresy in Rome July July 2 - Battle of Nieuwpoort: Dutch forces under Maurice of Nassau defeat Spanish forces under Archduke Albert in a battle on the... Events March 18 - Sissinios formally crowned Emperor of Ethiopia May 14 - Protestant Union founded in Auhausen. ... In the history of science, the scientific revolution was the period that roughly began with the discoveries of Kepler, Galileo, and others at the dawn of the 17th century, and ended with the publication of the Philosophiae Naturalis Principia Mathematica in 1687 by Isaac Newton. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... Sir Isaac Newton, PRS (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, and natural philosopher who is regarded by many as the most influential scientist in history. ... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ...

See also

• Indian mathematics
• Indian mathematicians
• History of mathematics

Indian contributions to mathematics include 1. ... Here is a chronology of the main Indian mathematicians: BC Yajnavalkya, 1800 BC, the author of the altar mathematics of the Shatapatha Brahmana. ... The word mathematics comes from the Greek μάθημα (máthema) which means science, knowledge, or learning; μαθηματικός (mathematikós) means fond of learning. Today, the term refers to a specific body of knowledge - the rigorous, deductive study of numbers, shapes, patterns, and change. ...

External links

• Indian Mathematics: Redressing the balance
• Keralese mathematics
• Possible transmission of Keralese mathematics to Europe
• The Kerala School, European Mathematics and Navigation
• Neither Newton nor Leibnitz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala